{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from statsmodels.tsa import stattools\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Start by setting the current directory and henceforth working relative to it\n",
    "os.chdir('D:/Practical Time Series')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nThis notebook illustrates time series decomposition by moving averages.\\nBoth additive and multiplicative models are demonstrated.\\n'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "This notebook illustrates time series decomposition by moving averages.\n",
    "Both additive and multiplicative models are demonstrated.\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nLet us demonstrate the addtive model using US Airlines monthly miles flown dataset.\\n'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Let us demonstrate the addtive model using US Airlines monthly miles flown dataset.\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#read the data from into a pandas.DataFrame\n",
    "air_miles = pd.read_csv('datasets/us-airlines-monthly-aircraft-miles-flown.csv')\n",
    "air_miles.index = air_miles['Month']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of the DataFrame: (97, 2)\n"
     ]
    }
   ],
   "source": [
    "#Let's find out the shape of the DataFrame\n",
    "print('Shape of the DataFrame:', air_miles.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Month</th>\n",
       "      <th>U.S. airlines: monthly aircraft miles flown (Millions) 1963 -1970</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1963-01</th>\n",
       "      <td>1963-01</td>\n",
       "      <td>6827.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-02</th>\n",
       "      <td>1963-02</td>\n",
       "      <td>6178.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-03</th>\n",
       "      <td>1963-03</td>\n",
       "      <td>7084.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-04</th>\n",
       "      <td>1963-04</td>\n",
       "      <td>8162.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-05</th>\n",
       "      <td>1963-05</td>\n",
       "      <td>8462.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-06</th>\n",
       "      <td>1963-06</td>\n",
       "      <td>9644.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-07</th>\n",
       "      <td>1963-07</td>\n",
       "      <td>10466.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-08</th>\n",
       "      <td>1963-08</td>\n",
       "      <td>10748.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-09</th>\n",
       "      <td>1963-09</td>\n",
       "      <td>9963.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1963-10</th>\n",
       "      <td>1963-10</td>\n",
       "      <td>8194.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Month  \\\n",
       "Month              \n",
       "1963-01  1963-01   \n",
       "1963-02  1963-02   \n",
       "1963-03  1963-03   \n",
       "1963-04  1963-04   \n",
       "1963-05  1963-05   \n",
       "1963-06  1963-06   \n",
       "1963-07  1963-07   \n",
       "1963-08  1963-08   \n",
       "1963-09  1963-09   \n",
       "1963-10  1963-10   \n",
       "\n",
       "         U.S. airlines: monthly aircraft miles flown (Millions) 1963 -1970  \n",
       "Month                                                                       \n",
       "1963-01                                             6827.0                  \n",
       "1963-02                                             6178.0                  \n",
       "1963-03                                             7084.0                  \n",
       "1963-04                                             8162.0                  \n",
       "1963-05                                             8462.0                  \n",
       "1963-06                                             9644.0                  \n",
       "1963-07                                            10466.0                  \n",
       "1963-08                                            10748.0                  \n",
       "1963-09                                             9963.0                  \n",
       "1963-10                                             8194.0                  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Let's see first 10 rows of it\n",
    "air_miles.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Let's rename the 2nd column\n",
    "air_miles.rename(columns={'U.S. airlines: monthly aircraft miles flown (Millions) 1963 -1970':\\\n",
    "                          'Air miles flown'\n",
    "                         },\n",
    "                inplace=True\n",
    "                )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of missing values found: 1\n"
     ]
    }
   ],
   "source": [
    "#Check for missing values and remove the row\n",
    "missing = pd.isnull(air_miles['Air miles flown'])\n",
    "print('Number of missing values found:', missing.sum())\n",
    "air_miles = air_miles.loc[~missing, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Let us estimate the trend component by 2X12 monthly moving average\n",
    "MA12 = air_miles['Air miles flown'].rolling(window=12).mean()\n",
    "trendComp = MA12.rolling(window=2).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Let us now compute the residuals after removing the trend component\n",
    "residuals = air_miles['Air miles flown'] - trendComp\n",
    "\n",
    "#To find the sesonal compute we have to take monthwise average of these residuals\n",
    "month = air_miles['Month'].map(lambda d: d[-2:])\n",
    "monthwise_avg = residuals.groupby(by=month).aggregate(['mean'])\n",
    "#Number of years for which we have the data\n",
    "nb_years = 1970-1963+1\n",
    "\n",
    "seasonalComp = np.array([monthwise_avg.as_matrix()]*nb_years).reshape((12*nb_years,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "#After deducting the trend and seasonal component we are left with irregular variations\n",
    "irr_var = air_miles['Air miles flown'] - trendComp - seasonalComp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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txyJiiu3GG2HTJkhLgyFD4J57CkdGx3GcvFBiTFsinfSoo6by1VfQsKFV5D17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\nf0fPkhowBMIVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x28f3ec8d780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the original time series, trend, seasonal and random components\n",
    "fig, axarr = plt.subplots(4, sharex=True)\n",
    "fig.set_size_inches(5.5, 5.5)\n",
    "\n",
    "air_miles['Air miles flown'].plot(ax=axarr[0], color='b', linestyle='-')\n",
    "axarr[0].set_title('Monthly air miles')\n",
    "\n",
    "pd.Series(data=trendComp, index=air_miles.index).plot(ax=axarr[1], color='r', linestyle='-')\n",
    "axarr[1].set_title('Trend component in monthly air miles')\n",
    "\n",
    "pd.Series(data=seasonalComp, index=air_miles.index).plot(ax=axarr[2], color='g', linestyle='-')\n",
    "axarr[2].set_title('Seasonal component in monthly air miles')\n",
    "\n",
    "pd.Series(data=irr_var, index=air_miles.index).plot(ax=axarr[3], color='k', linestyle='-')\n",
    "axarr[3].set_title('Irregular variations in monthly air miles')\n",
    "\n",
    "plt.tight_layout(pad=0.4, w_pad=0.5, h_pad=2.0)\n",
    "\n",
    "plt.savefig('plots/ch2/B07887_02_20.png', format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Run ADF test on the irregular variations\n",
    "adf_result = stattools.adfuller(irr_var.loc[~pd.isnull(irr_var)], autolag='AIC')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-val of the ADF test on irregular variations in air miles flown: 0.0657741102573\n"
     ]
    }
   ],
   "source": [
    "print('p-val of the ADF test on irregular variations in air miles flown:', adf_result[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nThe additive decompostion has been able to reduce the p-value\\nfrom 0.99 in case of the original time series\\n(as shown in Chapter_2_Augmented_Dickey_Fuller_Test.ipynb)\\nto 0.066 after decomposing.\\n'"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "The additive decompostion has been able to reduce the p-value\n",
    "from 0.99 in case of the original time series\n",
    "(as shown in Chapter_2_Augmented_Dickey_Fuller_Test.ipynb)\n",
    "to 0.066 after decomposing.\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nNow we will attempt decomposition of the original time\\nusing a multiplicative model\\n'"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Now we will attempt decomposition of the original time\n",
    "using a multiplicative model\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nComputation of the trend-cycle component remain same. But the seasonal component\\nis estimated as follows\\n'"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Computation of the trend-cycle component remain same. But the seasonal component\n",
    "is estimated as follows\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#We start with the residuals left after removing the trend component\n",
    "residuals = air_miles['Air miles flown'] / trendComp\n",
    "\n",
    "#To find the sesonal compute we have to take monthwise average of these residuals\n",
    "month = air_miles['Month'].map(lambda d: d[-2:])\n",
    "monthwise_avg = residuals.groupby(by=month).aggregate(['mean'])\n",
    "#Number of years for which we have the data\n",
    "nb_years = 1970-1963+1\n",
    "\n",
    "seasonalComp = np.array([monthwise_avg.as_matrix()]*nb_years).reshape((12*nb_years,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#After adjusting the trend and seasonal component we are left with irregular variations\n",
    "irr_var = air_miles['Air miles flown'] / (trendComp * seasonalComp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hB/OJ9OxpJqXy5YtPlp07YehQk6N9+739IWFUYdAgGDHCzFz16xefjI7jOAVl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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x28f3eaa8ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the original time series, trend, seasonal and random components\n",
    "fig, axarr = plt.subplots(4, sharex=True)\n",
    "fig.set_size_inches(5.5, 5.5)\n",
    "\n",
    "air_miles['Air miles flown'].plot(ax=axarr[0], color='b', linestyle='-')\n",
    "axarr[0].set_title('Monthly air miles')\n",
    "\n",
    "pd.Series(data=trendComp, index=air_miles.index).plot(ax=axarr[1], color='r', linestyle='-')\n",
    "axarr[1].set_title('Trend component in monthly air miles')\n",
    "\n",
    "pd.Series(data=seasonalComp, index=air_miles.index).plot(ax=axarr[2], color='g', linestyle='-')\n",
    "axarr[2].set_title('Seasonal component in monthly air miles')\n",
    "\n",
    "pd.Series(data=irr_var, index=air_miles.index).plot(ax=axarr[3], color='k', linestyle='-')\n",
    "axarr[3].set_title('Irregular variations in monthly air miles')\n",
    "\n",
    "plt.tight_layout(pad=0.4, w_pad=0.5, h_pad=2.0)\n",
    "\n",
    "plt.savefig('plots/ch2/B07887_02_21.png', format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Run ADF test on the irregular variations\n",
    "adf_result = stattools.adfuller(irr_var.loc[~pd.isnull(irr_var)], autolag='AIC')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-val of the ADF test on irregular variations in air miles flown: 0.000176452809084\n"
     ]
    }
   ],
   "source": [
    "print('p-val of the ADF test on irregular variations in air miles flown:', adf_result[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nVoila! The p-val has further reduced to 0.000176.\\nThe null hypothesis about non-stationarity of the irregular variations\\ncan be rejected at even a level of confidence of 99 % (alpha=0.01).\\nThis shows that the original time series has been de-stationarized to\\nthe stationary irregular variations. Besides we have estimates of both trend-cycle\\nand seasonal components.\\n'"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Voila! The p-val has further reduced to 0.000176.\n",
    "The null hypothesis about non-stationarity of the irregular variations\n",
    "can be rejected at even a level of confidence of 99 % (alpha=0.01).\n",
    "This shows that the original time series has been de-stationarized to\n",
    "the stationary irregular variations. Besides we have estimates of both trend-cycle\n",
    "and seasonal components.\n",
    "\"\"\""
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
